1)Using IEEE 754 representation for single precision floating point, give the 32- bit binary encoding for the numbers below. Show the sign, exponent, and mantissa (significand). a. -2.40625 b. 11.2265625 2) Given the following binary number: 1101.0111, what will be its decimal number equivalent?
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bit binary encoding for the numbers below.
Show the sign, exponent, and mantissa (significand).
a. -2.40625
b. 11.2265625
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- 1) Using IEEE 754 representation for single precision floating point, give the 32-bit binary encoding for the numbers below.Show the sign, exponent, and mantissa (significand).a. -2.40625b. 11.2265625 2) Given the following binary number: 1101.0111, what will be its decimal numberequivalent?2. Convert the following binary numbers to floating point format. Assume a binary format consisting of a sign bit (negative = 1), a base 2, 8-bit, excess-128 exponent, and 23 bits of mantissa, with the implied binary point to the right of the first bit of the mantissa.a. 110110.011011b. −1.1111001c. 0.1100×236d. 0.1100×2−36This problem covers floating-point IEEE format.(a) Assuming single precision IEEE 754 format, what is the binary pattern for decimal number -6.16?(b) Assuming single precision IEEE 754 format, what decimal number is represented by this word:0 01111100 01100000000000000000000(Hint: remember to use the biased form of the exponent.)
- 6. Using IEEE 754 representation for single precision floating point, give the 32-bit binary encoding for the numbers below. Show the sign, exponent, and mantissa (significand).b. 11.22656258. Add the following two 8-bit binary numbers, producing an 8-bit result. Indicate the status of the carry and overflow bits at the end of the addition by circling the appropriate choices. The space in between is only for readability. 1111 0010 + 1101 0110 ----------- Overflow? Yes or No Carry? Yes or NoComplete the following arithmetic operations in two's complement representation. What are the values of the carry and overflow flag? Assume a six-bit system. 3 + 21 = ?
- 6. Convert the following numbers from unsigned binary notation to decimal notation, and from 6-bit 2's complement notation to decimal notation: i) 110011, ii) 001101, iii) 101101 7. Show how each of the following floating point values would be stored using IEEE-754 single precision (be sure to indicate the sign bit, the exponent, and the significand fields): a. 12.5 b. −1.5 c. 0.75 d. 26.625 8. The following is a representation of a decimal floating value using IEEE-754 single precision. Find out the value in decimal. 0 10000011 10101000000...01. Assume numbers are represented in 8-bit two's complement Show the calculation of the following: a) 5 + 10 b) 5 – 10 c) -5 + 10 d)-5 – 10 2. Represent the following decimal numbers or values according to the given requirements: a) +4 in both binary sign/magnitude and two's complement b) -6 in both binary sign/magnitude and two's complement c) -85 in two's complement d) +52 in two's complement 3. Find the following differences using twos complement arithmetic: a) 001000 – 110111 b) 10100101 – 011110 c) 100100001011 – 101010110011 d) 10011011 – 10100101Question 6 a) The IEEE Standard 754 representation of a floating point number is given as: 01101110110011010100000000000000. Determine the binary value represented by this number. b) Convert each of the following 8-bit two’s complement binary values to decimal. i) 10110111(base 2) ii) 01001101(base 2) iii) 11010111(base 2) iv) 01110111(base 2) c) Discuss the differences between static RAM and dynamic RAM
- 1)Using IEEE 754 representation for single precision floating point, give the 32-bit binary encoding for the numbers below.Show the sign, exponent, and mantissa (significand).a. -2.40625b. 11.2265625Please solve only 4 part rest are already answered This problem covers floating-point IEEE 754 format. 1)List four floating-point operations that cause NaN to be created? 2) In the 32-bit (single precision) IEEE 754 format, what is the encoding for negative zero? 3) In the 32-bit (single precision) IEEE 754 format, what is the encoding for positive infinity? 4) Assuming 32-bit (single precision) IEEE 754 format, what decimal number is represent by this word: 1 01111101 001000000000000000000001. Assume we are using the simple model for floating-point representation discussed in the class (the representation uses a 14-bit format, 5 bits for the exponent with an Excess-M, a significand of 8 bits, and a single sign bit for the number) Convert -123.075 to the floating-point binary representation. 2. a) What is "Approximation Error" in floating-point representation? b) Why is it happening? c) How can we minimize it? d) How can the character codes be a solution for this?